# Graphs associated with nilpotent Lie algebras of maximal rank.

Eduardo Díaz; Rafael Fernández-Mateos; Desamparados Fernández-Ternero; Juan Núñez

Revista Matemática Iberoamericana (2003)

- Volume: 19, Issue: 2, page 325-338
- ISSN: 0213-2230

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topDíaz, Eduardo, et al. "Graphs associated with nilpotent Lie algebras of maximal rank.." Revista Matemática Iberoamericana 19.2 (2003): 325-338. <http://eudml.org/doc/39704>.

@article{Díaz2003,

abstract = {In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph of this digraph with every isomorphism class of nilpotent Lie algebras of maximal rank and of type A. Finally, we show an algorithm which obtains these subgraphs and also groups them in isomorphism classes.},

author = {Díaz, Eduardo, Fernández-Mateos, Rafael, Fernández-Ternero, Desamparados, Núñez, Juan},

journal = {Revista Matemática Iberoamericana},

keywords = {Teoría de grafos; Algebra de Lie; Algebra nilpotente; Singularidades; Geometría algebraica; nilpotent Lie algebra; maximal rank; directed graph},

language = {eng},

number = {2},

pages = {325-338},

title = {Graphs associated with nilpotent Lie algebras of maximal rank.},

url = {http://eudml.org/doc/39704},

volume = {19},

year = {2003},

}

TY - JOUR

AU - Díaz, Eduardo

AU - Fernández-Mateos, Rafael

AU - Fernández-Ternero, Desamparados

AU - Núñez, Juan

TI - Graphs associated with nilpotent Lie algebras of maximal rank.

JO - Revista Matemática Iberoamericana

PY - 2003

VL - 19

IS - 2

SP - 325

EP - 338

AB - In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph of this digraph with every isomorphism class of nilpotent Lie algebras of maximal rank and of type A. Finally, we show an algorithm which obtains these subgraphs and also groups them in isomorphism classes.

LA - eng

KW - Teoría de grafos; Algebra de Lie; Algebra nilpotente; Singularidades; Geometría algebraica; nilpotent Lie algebra; maximal rank; directed graph

UR - http://eudml.org/doc/39704

ER -

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